Question: Simplify the following expression: $ n = \dfrac{-7y - 6}{-6y + 5} + \dfrac{-7}{2} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-7y - 6}{-6y + 5} \times \dfrac{2}{2} = \dfrac{-14y - 12}{-12y + 10} $ Multiply the second expression by $\dfrac{-6y + 5}{-6y + 5}$ $ \dfrac{-7}{2} \times \dfrac{-6y + 5}{-6y + 5} = \dfrac{42y - 35}{-12y + 10} $ Therefore $ n = \dfrac{-14y - 12}{-12y + 10} + \dfrac{42y - 35}{-12y + 10} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-14y - 12 + 42y - 35}{-12y + 10} $ $n = \dfrac{28y - 47}{-12y + 10}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-28y + 47}{12y - 10}$